Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
4732.2-a1 |
4732.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4732.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{22} \cdot 7^{14} \cdot 13^{2} \) |
$1.96087$ |
$(a), (-a+1), (-2a+1), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.175111233$ |
0.264743301 |
\( -\frac{10824513276632329}{21926008832} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -4609\) , \( 120244\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-4609{x}+120244$ |
4732.2-b1 |
4732.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4732.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{13} \cdot 7^{2} \cdot 13^{2} \) |
$1.96087$ |
$(a), (-a+1), (-2a+1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.193322852$ |
0.902067286 |
\( \frac{14283778547303}{186368} a - \frac{4170573974757}{93184} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 124 a - 171\) , \( -803 a + 394\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(124a-171\right){x}-803a+394$ |
4732.2-b2 |
4732.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4732.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{23} \cdot 7 \cdot 13^{4} \) |
$1.96087$ |
$(a), (-a+1), (-2a+1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.193322852$ |
0.902067286 |
\( \frac{27512189178035}{4961861632} a + \frac{12113688444791}{2480930816} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 24 a + 27\) , \( -34 a + 147\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(24a+27\right){x}-34a+147$ |
4732.2-c1 |
4732.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4732.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{13} \cdot 7^{2} \cdot 13^{2} \) |
$1.96087$ |
$(a), (-a+1), (-2a+1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.193322852$ |
0.902067286 |
\( -\frac{14283778547303}{186368} a + \frac{5942630597789}{186368} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -125 a - 46\) , \( 802 a - 408\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-125a-46\right){x}+802a-408$ |
4732.2-c2 |
4732.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4732.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{23} \cdot 7 \cdot 13^{4} \) |
$1.96087$ |
$(a), (-a+1), (-2a+1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.193322852$ |
0.902067286 |
\( -\frac{27512189178035}{4961861632} a + \frac{51739566067617}{4961861632} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -24 a + 51\) , \( 34 a + 113\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-24a+51\right){x}+34a+113$ |
4732.2-d1 |
4732.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4732.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{14} \cdot 7^{2} \cdot 13^{10} \) |
$1.96087$ |
$(a), (-a+1), (-2a+1), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.211690204$ |
$0.533192753$ |
1.706459444 |
\( -\frac{1207949625}{332678528} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -22\) , \( 884\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-22{x}+884$ |
4732.2-e1 |
4732.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4732.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{50} \cdot 7^{3} \cdot 13^{2} \) |
$1.96087$ |
$(a), (-a+1), (-2a+1), (13)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5^{2} \) |
$1$ |
$0.220089901$ |
4.159308180 |
\( -\frac{117707714055526111767}{700388906893312} a - \frac{5825725329423279627}{350194453446656} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1938 a + 467\) , \( 34770 a - 41587\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-1938a+467\right){x}+34770a-41587$ |
4732.2-e2 |
4732.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4732.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{50} \cdot 7^{3} \cdot 13^{2} \) |
$1.96087$ |
$(a), (-a+1), (-2a+1), (13)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5^{2} \) |
$1$ |
$0.220089901$ |
4.159308180 |
\( \frac{117707714055526111767}{700388906893312} a - \frac{129359164714372671021}{700388906893312} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 1938 a - 1471\) , \( -34770 a - 6817\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(1938a-1471\right){x}-34770a-6817$ |
4732.2-e3 |
4732.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4732.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{40} \cdot 7^{6} \cdot 13^{4} \) |
$1.96087$ |
$(a), (-a+1), (-2a+1), (13)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 5^{2} \) |
$1$ |
$0.220089901$ |
4.159308180 |
\( \frac{71903073502287}{60782804992} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 866\) , \( 6445\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+866{x}+6445$ |
4732.2-e4 |
4732.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4732.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{20} \cdot 7^{12} \cdot 13^{8} \) |
$1.96087$ |
$(a), (-a+1), (-2a+1), (13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 5^{2} \) |
$1$ |
$0.110044950$ |
4.159308180 |
\( \frac{8511781274893233}{3440817243136} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -4254\) , \( 59693\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-4254{x}+59693$ |
4732.2-e5 |
4732.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4732.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{10} \cdot 7^{24} \cdot 13^{4} \) |
$1.96087$ |
$(a), (-a+1), (-2a+1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \cdot 5^{2} \) |
$1$ |
$0.055022475$ |
4.159308180 |
\( \frac{3389174547561866673}{74853681183008} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -31294\) , \( -2081875\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-31294{x}-2081875$ |
4732.2-e6 |
4732.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4732.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{10} \cdot 7^{6} \cdot 13^{16} \) |
$1.96087$ |
$(a), (-a+1), (-2a+1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5^{2} \) |
$1$ |
$0.055022475$ |
4.159308180 |
\( \frac{22868021811807457713}{8953460393696} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -59134\) , \( 5547693\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-59134{x}+5547693$ |
4732.2-f1 |
4732.2-f |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4732.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{2} \cdot 7^{6} \cdot 13^{2} \) |
$1.96087$ |
$(a), (-a+1), (-2a+1), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$3.051746300$ |
4.613806728 |
\( \frac{4019679}{8918} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 3\) , \( -5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+3{x}-5$ |
4732.2-g1 |
4732.2-g |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4732.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
$1.96087$ |
$(a), (-a+1), (-2a+1), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$0.868936999$ |
$0.256426207$ |
6.063650696 |
\( -\frac{424962187484640625}{182} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -15663\) , \( -755809\bigr] \) |
${y}^2+{x}{y}={x}^{3}-15663{x}-755809$ |
4732.2-g2 |
4732.2-g |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4732.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{6} \cdot 7^{6} \cdot 13^{6} \) |
$1.96087$ |
$(a), (-a+1), (-2a+1), (13)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$0.289645666$ |
$0.769278622$ |
6.063650696 |
\( -\frac{795309684625}{6028568} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -193\) , \( -1055\bigr] \) |
${y}^2+{x}{y}={x}^{3}-193{x}-1055$ |
4732.2-g3 |
4732.2-g |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4732.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{18} \cdot 7^{2} \cdot 13^{2} \) |
$1.96087$ |
$(a), (-a+1), (-2a+1), (13)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$0.096548555$ |
$2.307835866$ |
6.063650696 |
\( \frac{37595375}{46592} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 7\) , \( -7\bigr] \) |
${y}^2+{x}{y}={x}^{3}+7{x}-7$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.